Keywords

Circuital modeling, numerical procedures, transient
response

Abstract

We apply the proper eigenvalue procedure to a system of
two concentric rotating cylinders enclosing a viscous
fluid. The linear partial differential equations that rule the
system in the absence of gravity, and in the low Reynolds
limit, are solved a) analytically, b) through direct space
and time iteration, and c) by using the eigenvalue
procedure which avoids numerical time iterations. In this
method the time dependent response of the system is
obtained directly from the trivial Laplace transform
inversion, once the zeros and poles of the system are
known. The method arises from the analysis of the
Laplace transform of a given variable (the velocity of the
liquid in the present paper), as given by application of the
determinant rule according to Cramer. The determinants
involved are evaluated efficiently in terms of a
generalized eigenvalue problem, which determines the
poles and zeros for the system. We compare the
computational time required in the three approaches,
showing the advantages of the eigenvalue calculation.
This approach might be particularly useful in engineering
and science teaching in multidimensional problems since
it not only saves computer time, but also provides a
valuable physical insight through the knowledge of the
pole and zero constellation